Write an exponential function in the form y = ab that goes through points (0,18) and (3,6174).

Answer:

5 complete cups and 7/8 of a cup

A) Let the length of one piece be x. if one piece is 45 m longer than the other one, it means that the length of the other one would be (x + 45) m

Given that the total length of both pieces is 120m, then the equation would be

x + x + 45 = 120

2x + 45 = 120

2x = 120 - 45 = 75

x = 75/2

x = 37.5

Thus, the length of each piece are

37.5 m

37.5 + 45 = 82.5 m

B) The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(length + width)

Given that

length = 82.5

width = 37.5

then

perimeter = 2(82.5 + 37.5) = 2 * 120

perimeter of rectangle= 240 m

C) the formula for determining area of a rectangle is expressed as

Area = length * width

Area of rectangle = 82.5 * 37.5 = 3093.75 cm^2

The total number of triangles formed by joining vertices of 10-sided polygon is given by the combination of 10 sides taken at 3, i.e. selection of 3 points from 10 points ( because a triangle has 3 vertices). This gives

Then, the answer is the last option: 120

Answer:

32.50x + 7.50 < 235

Step-by-step explanation:

All the cost have to be less than 325.  x stands for the number of people buying tickets.

With each additional tree , the estimated time increases by 10 minutes .

in the question ,

a table with number of trees and time required to plant them is given .

For planting 1 tree 30 minutes is required to plant them .

for planting 2 trees 40 minutes is required to plant them .

increase in number of tree = 2 tree - 1 tree = 1 tree

change in time required = 40 min - 30 min = 10 min

for planting 3 trees , 50 minutes is required to plant them .

increase in number of tree = 3 trees - 2 trees = 1 tree

change in time required = 50 min - 40 min = 10 min

So, we can see that for every additional tree planted the time increases by 10 minutes .

Therefore , with each additional tree , the estimated time increases by 10 minutes .

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Answer:

23.4%

Step-by-step explanation:

[tex]\frac{18}{77} =\frac{x}{100}[/tex]

$18 divided by $77 is the equivalent of X(% spent on scarves) divided by 100. To find X you cross multiply and divide. [tex](18*100)/77=23.377...[/tex], rounded, X = 23.4

Total number of student 20.

Total number of fruits are 4.

The theoretical probability that a student will choose a banana is 0.25

The experimental probability is 1/20=0.05.

Thus there is a huge difference in the theoritical probability and experimental probability.

Thus the experimental probability get closer to the theoretical probability is:

A. only give two choices of fruit.

According to the given diagram, we have 4 shirts in total, where there's only one short-sleeve white shirt, so we just have to divide 1/4

Then, we multiply by 100 to express it in percentage

The correct option C: A rotation of ABC 180 counterclockwise around A, such that ABC maps to ADC.

For the given question;

In triangles ABC angle CAB is 47.

If the triangles ABC and ACD becomes congruent such that angle ACD corresponds to angles ABC.

Then, both angles will be equal.

For, this, a rotation of ABC 180 counterclockwise around A, such that ABC maps to ADC is to be done.

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The formula for the nth term is expressed as

an = (an - 1)^2 - 3

This is a recursive formula

This means that the second term, a2 is

a2 = (a2 - 1)^2 - 3

a2 = (a1)^2 - 3

a2 = 4^2 - 3 = 16 - 3 = 13

a3 = (a3 - 1)^2 - 3

a3 = (a2)^2 - 3

a3 = 13^2 - 3 = 169 - 3 = 166

a4 = (a4 - 1)^2 - 3

a4 = (a3)^2 - 3

a4 = 166^2 - 3 = 27556 - 3 = 27553

Thus,

a4 = 27553

The answer of the given equation is x = 1/4 or 0.25

We are given the equation:-

12x = 8x + 1

We have to solve the equation to find the value of x.

Rearranging the equation to get the like terms on the same side, we get,

12x - 8x = 1

4x = 1

x = 1/4

Hence, the value of x is 1/4 or 0.25.

Like terms

Like terms can be defined as terms that contain the same variables raised to the same power. Only the numerical coefficients are different. In an expression, only we can combine like terms.

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Step 1

Given data

Expression 1 = 3x + 5

Expression 2 =

Given:

Quantum Logic recently expanded its operations at a cost of $450,000.

So, P = 450,000

The rate of growth = r = 8% = 0.08

compounded quarterly, n = 4

We will find the future value of the investment (A) after t = 5 years

We will use the following formula:

Substitute with the given values:

So, the answer will be:

The future investment = $668,676.33

According to the problem, the principal is $1,000, the interest is 3% compounded monthly and the time is 8 years.

We have to use the compounded interest formula

Replacing the given information, we have

Now, we solve for A

Given:

Cost of each puppy = $200

Number of puppies = 8

Here, the equation for total cost of puppies will be:

C = 200x

Where x represents the number of puppies sold

Cost of 1 puppy = $200

Cost of 2 puppies = $200(2) = $400

Cost of 3 puppies = $200(3) = $600

If you continue with the pattern you'll see the graph has a rate of change of 200

To determine if the graph will be continuous or discrete, we have:

For a graph to be continuous, the points on the graph must be connected with a continuos line, while for a graph to be discrete the points are series of unconnected points just like in a scatter plot.

The graph of this will be a discrete graph. A discrete graph have set of values(points)

ANSWER:

B. discrete

Given the word problem, we can deduce the following information:

1. Liz collected 16 cans, which is 20% of her goal.

To determine the number of cans that Liz needs to collect to reach her goal, we use below equation:

where:

x= total number of cans that Liz needs to collect

So,

Hence, the total number of cans is 80.

A.

To complete the double number line, we must determine first the other percent values. It the goal is 100%, we must subtract 20% from 100% and divide it by 4 to get the remaining percent values. So,

So the other percent values are:

0%

20%

20%+20%=40%

40%+20%=60%

60%+20%=80%

80%+20%=100%

To determine the amount of cans for each percent value,the process is shown below:

Therefore, the answer for double number line is:

Cans : 0 16 32 48 64 80

Percent : 0% 20% 40% 60% 80% 100%

B.

Based on the information gathered from A, for every 16 cans Liz collects, she adds 20% toward her goal. She will have 32 cans if she reaches 40% of her goal. Liz must collect 80 cans to reach her goal.

Answer/Step-by-step explanation:

y = mx + b

Slope = m

 y₂ - y₁

---------- = m

 x₂ - x₁

----------------------------------------------------------------------------------------------------------

y - intercept = b

y - y₁ = m(x - x₁)

If there's an equation I can solve it, but I hope this helps!

When looking at a graph of a line, there are two things you should look for straight off the bat. First, the y-intercept. And second, the slope.

The equation of a line is y = mx + b, where m is the slope, b is the y-intercept, and x is the input.

What is slope?
Slope is a number that determines how the line changes. It is often referred to as the "rate of change" because it represents how much the y-value of the line changes when the input (x) changes. The formula for slope is:
[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
Breakdown: This formula represents the change in the line, typically left to right. It shows the change in x-value over the change in corresponding y-value. This is also known as "rise over run," because the y-value is how much the line changes vertically, while the x-value is how much it changes horizontally.

Example: Let's say our line has a slope of 4, or m = 4/1. This means the y-value will change 4 units when the x-value changes by 1.

What is y-intercept?
Y-intercept is a value that determines the location of the line. When x = 0, the value of b will be the y-value. Essentially, when the line crosses the y-axis, that will be the y-value of the line.

Whne the coordinates are reflected over y -axis, then the coordinates are (x,y) = (-x,y)

.

The coodinates of A(3,0) and after reflection A'(-3,0)

The coordinates B(1,4) and after reflection B'(-1,0)

The coordinates C(5,3) and after reflection C'(-5,3)

Plot the image on the graph

Let's recall that If a set of 2 parallel lines, line m and line m, are crossed or cut by another line, line T, in our question, we say "a set of parallel lines are cut by a transversal.

Each of the parallel lines cut by the transversal has 4 angles surrounding the intersection.

These are matched in measure and position with a counterpart at the other parallel line.

At each of the parallel lines, there are two pairs of vertical angle. Each angle in the pair is congruent to the other angle in the pair.

In our question, the angle that measures 145 degrees is congruent with the opposites angles of angle x.

Let's recall that x and 145 degrees are adjacent supplementary angles. And these angles add up to 180 degrees. Then, for solve for x, we have:

x = 180 - 145

x = 35 degrees

To factor an expression of the form:

we need to find two integers a and b that fullfil:

then we write the expression as:

and factor by agrupation.

Let's do this with the expression:

In this case B=-17 and C=42.

If we take a=-14 and b=-3, then:

then we write the expression as:

Therefore, the factorize expression is:

From the diagram,

CD is corresponding to WR

VW is corresponding to BC

RS is corresponding to DE

ST is corresponding to EF

TU is corresponding to FA

Final answer

Answer

x = 2, and y = 3

Explanation:

given the following linear equation

7x - 6y = -4------------- equation 1

14x + 5y = 43 ---------- equation 2

This equation can be solve simultaneously by using elimination method

Step 1 : eliminate x

To eliminate x, multiply equation 1 by 2 qnd equation 2 by 1

7x * 2 - 6y * 2 = -4 * 2

14x * 1 + 5y * 1 = 43 * 1

14x - 12y = -8 ----------------- equation 3

14x + 5y = 43------------------ equation 4

Substract equation 4 from3

(14x - 14x) - 12 - 5y = -8 - 43

0 - 17y = -51

-17y = -51

Divide both sides by -17

-17y/-17 = -51/-17

y = 51/17

y = 3

To find x, put the value of y into equation 1

7x - 6y = -4

7x - 6(3) = -4

7x - 18 = -4

Collect the like terms

7x = -4 + 18

7x = 14

Divide both sides by 7

7x/7 = 14/7

x = 2

Therefore, x = 2 and y = 3

Given:

The function f(x) = 3cos(x) - 2.

Required:

What are the minimum and maximum value of function?

Explanation:

To check maximum and minimum value of function.

First derivate the original function.

After putting first derivative equal to zero, critical points can be found.

Then, do second deritvative to check points of maxima and minima.

The critical points at which second derivative greater than zero. Point will be of minima.

The critical points at which second derivative less than zero. Point will be of maxima.

So,

Now, do second derivative test for maximum and minimum points

Answer:

There is not enough evidence to support the claim that there is a linear correlation between the weights of discarded paper and glass for a significance level of α = 0.05.

Given,

A data set includes weights of garbage discarded in one week from 62 different households.

significance level of α=0.05.

Now, According to the question:

The correlation​ matrix provided is:

Variables    Paper     Glass

 Paper           1         0.1853

Glass        0.1853         1

The hypothesis for the test is:

H₀: ρ = 0 vs. H₀: ρ ≠ 0

The test statistic is:

r = 0.1983 ≈ 0.198

As the alternate hypothesis does not specifies the direction of the test, the test is two tailed.

The critical value for the two-tailed test is:

[tex]r_{alpha}/2, (n -2) = r_{0.005}/2 ,(62-2) = 0.250[/tex]

The conclusion is:

Because the absolute value of the test statistic is less than the positive critical value, there is not enough evidence to support the claim that there is a linear correlation between the weights of discarded paper and glass for a significance level of α = 0.05.

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Given:

The two-way table represents the number of clubs that two hundred high school students

We will find the probability that a student will be in two clubs only and a girl

From the table, we will select the number that represents the number of girls that will be in the two clubs

so, the number = 68

the total number of students = 200

So, the probability will be =

So, the answer will be 34%

therefore, the answer is 70.08

Explanation

Step 1

first multiply as if there is no decimal

Step 2

count the number of digits after the decimal in each factor.

Step 3

Put the same number of digits behind the decimal in the product

therefore, the answer is 70.08

I hope this helps you

Answer: ∠ABD = 19°

Step-by-step explanation:

The angle formed by ABC is a complementary angle. This means the sum of both angles adds up to 90 degrees.

Since angle DBC is 71 degrees, 90 - 71 equals ∠ABD

90 - 71 = 19

Therefore ∠ABD = 19°

Answer:

m∠ABD = 19°

Step-by-step explanation:

Hello!

Recall that all angles of a rectangle are 90° in measure.

Angle B is 90°, and is made up of angles ABD and DBC.

We know the measure of angle DBC, it's given as 71°. We can find the measure of ABD by subtracting 71° from 90°.

So the measure of angle ABD is 19°.

Given:

Angle subtended at the center = 135 degrees

radius (r) = 4 yd

Solution

The formula for the length (l) of an arc is given as:

When we substitute the given parameters, we can find the length (l) of the arc:

Answer: 9.4 yd or 3.0 pi